Exam 2 Flashcards
Hypothesis
a theory about how the world works
- proposed as an explanation for data
- posed as statement about population parameters
Hypothesis testing
a method that used inferential statistics which of two hypothesis data support
likelihood
probability distribution of a statistic, according to each hypothesis
–if result is likely according to a hypothesis, we say data “support” or “are consistent with” the hypothesis
binary data
a set of two-choice outcomes
yes/no
binomial variable
a statistic for binary samples
– frequency of “yes” or “no”
binomial distribution
probability distribution for a binomial variables
null hypothesis
nothing interesting going on, blind chance
alternative hypothesis
one outcome more likely than expexed by chance
critical value
value or statistic must exceed to reject null hypothesis (luck)
sign test
ignore magnitude of change; just direction
–same logic as other binomial tests
Type 1 error
null hypothesis is true, but we reject it
– conclude a useless treatment is effective
Type II error
null hypothesis is false, but we don’t reject it
– don’t recognize when a treatment is effective
Type I error rate
proportion of times, when null hypothesis is true, that we mistakenly reject it
—Fraction of bogus treatments that we conclude are effective
Alpha Level
Chosen type I error rate
- -Usually .05 in Psychology
- -Determines critical value
Replication
- -doing exactly the same experiment but with a new sample
- -sampling variability means each replication will result in different value of statistic
Sampliing distribution
the probability distribution of some statistic over repeated replication of an experiment
distribution of sample means
the probability distribution for M
Standard Error
Typical distance from M to MEW
Law of Large Numbers
The larger the sample the closer M will be to MEW
Formally : as n goes to infinity, SE goes to 0
Central Limit Theorum
Characterized distribution of sample mean
–works for any population distribution
Distribution of sample variances
Probability distribution for s over repeated replication
Chi-Square
probability distribution for sampel variance
–positive skew; variance sensitive to outliers
t statistic
deviation of sample means divided by estimated standard error
t distribution
sampling distribution of t statistic
–derived from ration of Normal and modified x (squared)
t-test
Steps of t-test
1. State clearly the two hypotheses
2. Determine null and alternative hypotheses
H0: µ = µ0
H1: µ ≠ µ0
3. Compute the test statistic t from the data
t = M −µ0
s n
4. Determine likelihood function for test statistic according to H0
t distribution with n-1 degrees of freedom
5. Find critical value
R: qt(alpha,n-1,lower.tail=FALSE)
6. Compare actual result to critical value
t < tcrit: Retain null hypothesis, µ = µ0
t > tcrit: Reject null hypothesis, µ ≠ µ0
degrees of freedom
df = n -1
test statistic
statistic computed from sample to decide between hypotheses
–relevant to hypotheses being tested
critical region
Range of value that will lead to rejecting null hypothesis
– all values beyond critical value
Type II error rate
If the null is false, probability of failing to reject it
–depends on how false the null is
p-value
probability of getting a value equal to or more extreme than what you actually
–cumulative distribution or quantile within sampling distribution
Independent samples t-test
often interested in whether two groups have same mean
Mean Squares
Average of squared deviations
–Used for estimating variance population
Paired-Samples T-test
Data are pairs of scores (Xa, Xb)
–Form two samples, Xa and Xb
–Samples are not independent
Same null hypothesis as with independent samples
Approach
–Compute difference scores, Xdiff = Xa-Xb
Difference score (For paired samples t test)
Xdiff = Xa - Xb
Effect Size
if there is an effect, how big is it?
—How different is mew from mew not or mew A from mew b etc
Point Estimate
We don’t know exact effect size; samples just provide an estimate
Standardized Effect Size
Interpreting effect size depends on variable being measured
—Improving digit span by 2 more important than IQ
Solution: measure effect size relative to variability in raw scores
